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Heat Kernel estimates for some elliptic operators with unbounded diffusion coefficients
1. | Dipartimento di Matematica “Ennio De Giorgi”, Università del Salento, C.P.193, 73100, Lecce, Italy, Italy |
References:
[1] |
A. Bazan and W. Neves, The Caffarelli-Kohn-Niremberg's inequality for arbitrary norms, preprint. |
[2] |
A. Bazan and W. Neves, The Hardy and Caffarelli-Kohn-Niremberg inequalities revised, preprint, arXiv:1007.2005v1. |
[3] |
D. Bakry, F. Bolley, I. Gentil and P. Maheux, Weighted Nash inequalities, preprint, arXiv:1004.3456. |
[4] |
E. B. Davies, "One-Parameter Semigroups," London Mathematical Society Monographs, 15, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London-New York, 1980. |
[5] |
E. B. Davies, "Heat Kernels and Spectral Theory," Cambridge Tracts in Mathematics, 92, Cambridge University Press, Cambridge, 1989. |
[6] |
K.-J. Engel and R. Nagel, "One-Parameter Semigroups for Linear Evolutions Equations," Graduate Texts in Mathematics, 194, Springer-Verlag, New York, 2000. |
[7] |
S. Fornaro and L. Lorenzi, Generation results for elliptic operators with unbounded diffusion coefficients in $L^p$- and $C_b$-spaces, Discrete and Continuous Dynamical Systems, 18 (2007), 747-772. |
[8] |
G. Metafune, E. M. Ouhabaz and D. Pallara, Long time behavior of heat kernels of operators with unbounded drift terms, J. Math. Anal. Appl., 377 (2011), 170-179.
doi: 10.1016/j.jmaa.2010.10.023. |
[9] |
G. Metafune and C. Spina, Elliptic operators with unbounded diffusion coefficients in $L^p$ spaces, Ann. Sc. Norm. Super. Pisa Cl. Sci., to appear. |
[10] |
G. Metafune and C. Spina, Kernel estimates for a class of Schrödinger semigroups, Journal of Evolution Equations, 7 (2007), 719-742.
doi: 10.1007/s00028-007-0338-3. |
[11] |
G. Metafune, D. Pallara and M. Wacker, Feller semigroups on $\mathbb{R}^{N}$, Semigroup Forum, 65 (2002), 159-205.
doi: 10.1007/s002330010129. |
[12] |
B. Muckenhoupt, Hardy's inequalities with weights, Studia Math., 44 (1972), 31-38. |
[13] |
B. Muckenhoupt and R. Wheeden, Weighted norm inequalities for fractional integrals, Trans. Amer. Math. Soc., 192 (1974), 261-274.
doi: 10.1090/S0002-9947-1974-0340523-6. |
[14] |
E. M. Ouhabaz, "Analysis of Heat Equations on Domains," London Mathematical Society Monographs Series, 31, Princeton University Press, Princeton, NJ, 2005. |
[15] |
F.-Y. Wang, Functional inequalities and spectrum estimates: The infinite measure case, J. Funct. Anal., 194 (2002), 288-310.
doi: 10.1006/jfan.2002.3968. |
show all references
References:
[1] |
A. Bazan and W. Neves, The Caffarelli-Kohn-Niremberg's inequality for arbitrary norms, preprint. |
[2] |
A. Bazan and W. Neves, The Hardy and Caffarelli-Kohn-Niremberg inequalities revised, preprint, arXiv:1007.2005v1. |
[3] |
D. Bakry, F. Bolley, I. Gentil and P. Maheux, Weighted Nash inequalities, preprint, arXiv:1004.3456. |
[4] |
E. B. Davies, "One-Parameter Semigroups," London Mathematical Society Monographs, 15, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London-New York, 1980. |
[5] |
E. B. Davies, "Heat Kernels and Spectral Theory," Cambridge Tracts in Mathematics, 92, Cambridge University Press, Cambridge, 1989. |
[6] |
K.-J. Engel and R. Nagel, "One-Parameter Semigroups for Linear Evolutions Equations," Graduate Texts in Mathematics, 194, Springer-Verlag, New York, 2000. |
[7] |
S. Fornaro and L. Lorenzi, Generation results for elliptic operators with unbounded diffusion coefficients in $L^p$- and $C_b$-spaces, Discrete and Continuous Dynamical Systems, 18 (2007), 747-772. |
[8] |
G. Metafune, E. M. Ouhabaz and D. Pallara, Long time behavior of heat kernels of operators with unbounded drift terms, J. Math. Anal. Appl., 377 (2011), 170-179.
doi: 10.1016/j.jmaa.2010.10.023. |
[9] |
G. Metafune and C. Spina, Elliptic operators with unbounded diffusion coefficients in $L^p$ spaces, Ann. Sc. Norm. Super. Pisa Cl. Sci., to appear. |
[10] |
G. Metafune and C. Spina, Kernel estimates for a class of Schrödinger semigroups, Journal of Evolution Equations, 7 (2007), 719-742.
doi: 10.1007/s00028-007-0338-3. |
[11] |
G. Metafune, D. Pallara and M. Wacker, Feller semigroups on $\mathbb{R}^{N}$, Semigroup Forum, 65 (2002), 159-205.
doi: 10.1007/s002330010129. |
[12] |
B. Muckenhoupt, Hardy's inequalities with weights, Studia Math., 44 (1972), 31-38. |
[13] |
B. Muckenhoupt and R. Wheeden, Weighted norm inequalities for fractional integrals, Trans. Amer. Math. Soc., 192 (1974), 261-274.
doi: 10.1090/S0002-9947-1974-0340523-6. |
[14] |
E. M. Ouhabaz, "Analysis of Heat Equations on Domains," London Mathematical Society Monographs Series, 31, Princeton University Press, Princeton, NJ, 2005. |
[15] |
F.-Y. Wang, Functional inequalities and spectrum estimates: The infinite measure case, J. Funct. Anal., 194 (2002), 288-310.
doi: 10.1006/jfan.2002.3968. |
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